Various observation enhancing devices exist for viewing a subject. In general, the device transforms the subject and provides a distorted image which is viewed. More accurately, the transformed subject is further distorted by noise in electronics involved, optical noise from surrounding light, and/or quantum noise of random photons. Thus, the viewed image is a transformed, imperfect version of the subject as illustrated in FIG. 1.
The subject 7 is mathematically represented as a function f. The observation enhancing device 9 transforms or distorts the subject 7 by a function k. The generated image 11 (referenced as g) is viewed as an array of measured data points g.sub.i which includes a noise or measurement error factor .epsilon.. The distorted image is then stated mathematically as ##EQU1## That is, each point or pixel i in the viewed image g involves a sum of the light contributed from other neighboring points x on the subject 7 and an unknown noise or measurement error .epsilon..sub.1. The sum is over the set D of viewed points image.
In accordance with this contribution, a 3-D subject introduces a further complication. In addition to light contributed from neighboring points on the same plane, a 2-D slice or a view of a plane through the 3-D subject is blurred by light contributed to the viewed plane from neighboring planes. Hence, the distortion becomes a more complex problem.
Various devices and schemes have been developed to define and subsequently reverse such distortion to provide what is called a restored image of the subject. Some of the schemes involve a matrix of measured points which define the distortion and noise or measurement error. The matrix is inverted to provide a restored image. These schemes, however, are typically cumbersome and unsuitable for images with hundreds of data points or more.